Ann Margrock (special guest star Ann-Margret, providing her own voice) comes to town for a big concert and stays with the Flintstones, who do not know who she is. After a few tries, Fred and Barney both get on the Ann Margrock Show.

Note: During this season, ABC moved the series from Thursdays to Friday nights.

Arnold the paper boy annoys Fred as he is playing with Pebbles when he jokes that they will get married when they grow up. Fred then has a bad dream that Arnold grows up and becomes the local hero then takes his job at the quarry, his pride as a pool player and bowler, his friendship with Barney, and marries Pebbles.

Fred, tired of Barney and Betty constantly visiting to see Pebbles, kicks them out of the Flintstones' home. They then decide want a baby badly, so they wish upon a falling star and the next morning a baby boy is found in a basket on their door step. They named him Bamm Bamm because of his extreme strength. Barney and Betty soon take steps to legally adopt him. After almost being turned down, they are given the baby.

Fred mistakenly forgets Dino's birthday, but gets gifts for Pebbles. Dino gets jealous and Fred drags Dino outside. The next day, Dino is missing. Fred and Barney search for Dino, and they think he's been kidnapped by a man and according to the man, his name is "Rocky" and he is a stunt/dancing animal and they plan to get him back. Later at night, Fred and Barney takes "Rocky" and are chased by cops and they wind up in court and the real Dino pops up in court while being chased by dogcatchers.

Fred gets eyeglasses and takes the wrong ones. He then mistakes a monkey for Pebbles at the circus.

Fred and Barney enter a singing contest as the Flintstone Canaries on the "Hum Along with Herman Show".

Note: This episode is a spoof of the then-popular NBC TV series Sing Along With Mitch, starring Mitch Miller.

Fred and Barney get glued together on Barney's new bowling ball after Fred invents a new super-strong superglue.

Fred tries out for a Major League Baseball team. Fred is injured during his tryout while his friend Roger Marble. When Roger is picked, he is mistaken for Fred who, after much pressure, comes clean.